Fiber volume fraction

The fiber volume fraction or fiber volume content is the ratio of the volume of the fibers to the total volume of a fiber-reinforced material. It is abbreviated with . The fiber volume fraction is calculated analogously to the volume fraction of a two-phase mixture. It is an important parameter for fiber-plastic composites such as B. carbon fiber reinforced plastic (CFRP) or glass fiber reinforced plastic (GRP) . ${\ displaystyle \ varphi}$

In the laminate design, a fiber volume fraction of 60%, consequently a matrix volume fraction of 40%, has proven to be suitable as a standard. Higher fiber proportions are disadvantageous because the fibers are already so dense that not all of them are wetted by the matrix . You can also say that the laminate is “too dry”.

calculation

The fiber volume fraction results from the formula of the general volume fraction

${\ displaystyle \ varphi = {\ frac {V _ {\ text {fiber}}} {V _ {\ text {composite}}}} = {\ frac {V _ {\ text {fiber}}} {V _ {\ text { Fiber}} + V _ {\ text {matrix}} (+ V _ {\ text {spaces}})}}.}$

Importance in the design of fiber-plastic composites

When designing components, it is essential to specify the fiber volume percentage. Without this information, the basic elasticity parameters and the strength of the component cannot be determined. This means that fiber-plastic composites differ fundamentally from metallic materials. Wall thicknesses or cross-sections are usually dimensioned there. In the case of fiber-plastic composites, the amount of fibers is designed. The fiber volume fraction results from the amount of matrix used, and this is what determines the wall thickness of the component.

In the case of components that are at risk of stability, a low proportion of fiber volume is often advantageous. While, e.g. B. in plate buckling, the modulus of elasticity is linearly related to the buckling value , the wall thickness is cubic in the critical load.

For the oscillating stress in the fiber-parallel direction, low fiber volume fractions are also advantageous. Most of the fibers touch each other in the closest packing. The points of contact between the fibers act as internal flaws, from which cracks grow when exposed to vibrations.

Elongation enlargement

The fiber volume share has a significant influence on the so-called elongation increase . The increase in elongation is responsible for the poor static strength of fiber-plastic composites under stress perpendicular to the fiber.

Pack models

Maximum packing density. left: square packing, right: hexagonal packing

Depending on the underlying packaging model, there is a physical limit beyond which the fiber volume fraction cannot be increased. The following limits apply:

• square packing: ${\ displaystyle \ varphi _ {\ max} = {\ frac {\ pi} {4}} \ approx 0 {,} 79}$
• hexagonal packing: ${\ displaystyle \ varphi _ {\ max} = {\ frac {\ pi} {\ sqrt {12}}} \ approx 0 {,} 91}$

Since the packaging model can hardly be influenced during production, a mixture of both packaging models is achieved. The packing tends to be square rather than hexagonal.

Experimental investigation

The fiber volume fraction can be subsequently determined on components using various methods. This is particularly important in the course of quality assurance of composite components.

Ignition residue

In this process, a material sample is exposed to high temperatures. This burns the matrix, but the reinforcing fibers are retained. With known densities, the fiber volume fraction can be calculated by weighing the fibers. This method is only suitable for composites in which the matrix can be thermally decomposed and the thermal decomposition points of fiber and matrix are far apart.

Chemical extraction

By chemical extraction, e.g. B. with the help of an acid, either the matrix or the fiber is removed from the sample. After subsequent drying and weighing, the fiber volume fraction can be calculated with known densities. For many plastics reinforced with organic fibers, this is often the only way to determine the fiber volume fraction experimentally.

Counting out

A section with a known cross-sectional area is created from a sample volume. This section is then examined using a microscope. The areas of all fibers are added up using suitable methods. The fiber volume fraction is thus obtained directly.

Fiber mass fraction

The fiber mass fraction is a quantity related to the fiber volume fraction and must not be confused with it. He is z. B. needed to determine the mixed price of a fiber composite. According to VDA 260 , the fiber mass fraction is defined in percent by weight. Similarly, the fiber volume fraction is given in percent by volume, mostly containing up to 3% air.